The Risk and Risk-free Rate of T-bills

This study argues that a payment’s risk approaches zero as maturity approaches zero, and that the central bank’s short-term rate best captures the risk-free rate of various assets. Expecting that the T-bill risk largely reflects a country’s inflation risk or macrorisk, we measure the risk as a one-year payment’s risk to be comparable across various assets. We that the risk-free rate reflects the expected inflation effect, and that the inflation risk reflects the unexpected inflation effect or the investment opportunity cost. To simplify the formulas, we also examine if the two returns can be computed independently. We employ two factors to model the risk-free rate, which the market expects the current monetary policy to bring towards the neutral level over a certain period. The 4-factor models include a risk constant over maturity to capture the depreciation cost of inter-bank short-term lending. We thus use different models to split T-bill returns into the risk and the risk-free rate with repeated trials to minimize the prediction errors, thereby solving the model factors. The 4-factor independence model outperforms all the other models on average explaining 99.3% of the US T-bill returns. The T-bill metrics is the gateway to the risks of various corporate assets. We have to develop the 4-factor independence model into software to analyze the noise of the risk and the risk-free rate that follows a blended normal distribution of Nie (2023).